Find the four term of the AP whose sum is 28 and product of the extremes is 40
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Suppose the terms of A.P. be :-
a-2d,a-d,a+d,a+2d
so
- a-2d+a-d+a+d+a+2d =28
- gives
- 4a = 28
- a = 7
- now
- product of extremes :-
- (a-2d)(a+2d) = 40
- a² - 4d² = 40
- 7² - 4d² = 40
- 49 - 4d² = 40
- 49 - 40 = 4d²
- 9 = 4d²
- d² = 9/4
- d = √9/4
- d = 3/2
- so
- four terms are :-
a-2d = 7-2(3/2)=7-3=4
a-d = 7-3/2 = 7-1.5 = 5.5
a+d = 7+3/2 = 7+1.5 = 8.5
a+2d = 7+3 = 10
hope it helps
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